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Citation - WoS: 9
Citation - Scopus: 8
Similarity Solutions To Burgers' Equation in Terms of Special Functions of Mathematical Physics
(Jagellonian University, 2017) Öziş, Turgut; Aslan, İsmail
In this paper, the Lie group method is used to investigate some closed form solutions of famous Burgers' equation. A detailed and complete symmetry analysis is performed. By similarity transformations, the equation is reduced to ordinary differential equations whose general solutions are written in terms of the error function, Kummer's confluent hypergeometric function Φ(a; b; x) and Bessel functions Jp, showing the strong connection between the best mathematical modelling equations and the special functions of mathematical physics.
Citation - WoS: 32
Citation - Scopus: 37
Symbolic Computation and Construction of New Exact Traveling Wave Solutions To Fitzhugh-Nagumo and Klein-Gordon Equations
(Walter de Gruyter GmbH, 2009) Öziş, Turgut; Aslan, İsmail
With the aid of the symbolic computation system Mathematica, many exact solutions for the Fitzhugh-Nagumo equation and the Klein-Gordon equation with a quadratic nonlinearity are constructed by an auxiliary equation method, the so-called (G'/G)-expansion method, where the new and more general forms of solutions are also obtained. Periodic and solitary traveling wave solutions capable of moving in both directions are observed.

Mathematics / Matematik